Quiz #8 Vector 1) Given A(1, 2), and B( 3, 4), calculate A B 2) Given A( 1, 4, 3), and B( 3, 4, 1), calculate A B 3) Given the following magnitude of forces in Figure 1: α = 20, θ = 60, β = 30, F 1 = 1N, F 2 = 2N, F 3 = 3N, F 4 = 4N, N = 5N,, and the displacement r = 2.5m, calculate F r, such that F = F1 + F 2 + F 3 + F 4 + N Figure 1: 4) Given the following magnitude of forces in Figure 1: α = 20, θ = 60, β = 30, γ = 45, F 1 = 1N, F 2 = 2N, F 3 = 3N, F 4 = 4N, N = 5N,, and the displacement r = 2.5m, calculate F r, such that F = F1 + F 2 + F 3 + F 4 + N 1
Figure 2: An object of mass 3kg is released from rest on an incline plane (30 degrees from the horizontal) and from a vertical height of 15 meters above the ground as in Figure 3. Figure 3: 5) What is its velocity at the bottom of the plane? If, instead of being released from rest, the object is given an initial velocity of 10 m/s up along the incline plane, 6) what is its velocity at the bottom of the plane? If, instead of being released from rest, the object is given an initial velocity of 10 m/s down along the incline plane, 7) what is its velocity at the bottom of the plane? 2
If the object is released from rest and there is now friction between the plane and the object (µ s = 0.2, nd µ k = 0.1). 8) What is its velocity at the bottom of the plane? If the object is released from rest and there is still friction between the plane and the object but this time, it is released from a distance of 15m from the ground along the surface. 9) What is its velocity at the bottom of the plane? An object of mass 3kg is released from rest at a vertical distance h = 2m as in Figure 4. Figure 4: 10) What is the maximum compression of the spring (k = 200N/m) if the horizontal frictionless distance d is 4m? 11) What is the maximum compression of the spring (k = 200N/m) if the horizontal distance d is 4m and now has friction on it (µ s = 0.5, nd µ k = 0.4)? An object of mass 3kg is released from rest on an incline plane (30 degrees from the horizontal) and slides down over a distance of 5m along the plane before touching and compressing the plane as in Figure 5. The spring is initially uncompressed. 3
Figure 5: 12) If there is no friction, what is the maximum compression of the spring (k = 1000N/m)? 13) If there is friction (µ s = 0.2, nd µ k = 0.1) on the incline plane (but not under the spring), what is the maximum compression of the spring (k = 1000N/m) - keep 4 significant figures? 14) If there is friction (µ s = 0.2, nd µ k = 0.1) on the incline plane (and under the spring), what is the maximum compression of the spring (k = 1000N/m)keep 4 significant figures? 15) If there is friction (µ s = 0.2, nd µ k = 0.1), how far up along the inclined plane, an starting from the uncompressed end of the spring, does the object slide back up (k = 1000N/m)? 16) Provide Newton s first law in its mathematical form. 17) Provide Newton s second law in its mathematical form. 18) Provide Newton s third law in its mathematical form. 19) What is the energy conservation law expressed in its mathematical form? 20) What is the kinetic energy expressed in its mathematical form? 21) What is the potential energy due to gravity expressed in its mathematical form? 22) What is the potential energy due to a spring expressed in its mathematical form? 23) Provide the magnitude of the force due to a spring (Hooke s law) in its mathematical form. 24) Provide the definition of work in its mathematical form. 25) Provide the units for Forces. 4
26) Provide the units for Work. 27) Provide the units for Energy. Given m A = 4kg, m B = 3kg, α = 50, β = 30, µ s = 0.6, and µ k = 0.2 for an Atwood System of type IV in Figure 6: 28) Identify and state all the massive systems that you will be applying Newton s laws onto. Friction is present, so based on the given information and the question asked, state clearly the following: 29) which Newton Law(s) do you have to use. 30) Which frictional force is present and in what direction does it need to be? 31) Provide a Free Body Diagram for both systems A and B. 32) Provide all the equations obtained from your Free Body Diagrams. 33) Calculate the acceleration of the block A as it slides down the inclined plane. Figure 6: Given m A = 4kg, m B = 3kg, α = 50, β = 30, µ s = 0.7, and µ k = 0.2 such that friction is only between object A and the surface (there is no friction under object B) for an Atwood System of type IV in Figure 6 above: 34) Identify and state all the massive systems that you will be applying Newton s laws onto. Friction is present, so based on the given information and the question asked, state clearly the following: 35) Which Newton Law(s) do you have to use. 36) Which frictional force(s) are present and in what direction are they? 37) Provide a Free Body Diagram for both systems A and B. 38) Provide all the equations obtained from your Free Body Diagrams. 5
39) Calculate the magnitude of the friction between block A and the inclined plane if the system is at rest. Given m A = 4kg, m B = 3kg, β = 30, µ s = 0.6, and µ k = 0.2 such that friction is only between object A and the surface (there is no friction under object B) for an Atwood System of type IV in Figure 6 above: 40) Identify and state all the massive systems that you will be applying Newton s laws onto. Friction is present, so based on the given information and the question asked, state clearly the following: 41) Which Newton Law(s) do you have to use. 42) which frictional force and what direction needs to be used. 43) Provide a Free Body Diagram for both systems A and B. 44) Provide all the equations obtained from your Free Body Diagrams. 45) Calculate the maximum angle α for the system to remain at rest (the answer is obviously less than the value of α in the above question). A little algebra review: If you are facing the following equation: Asinα Bcosα C = 0 and you are after α. Move the sinα term by itself on one side of the equation, substitute it with 1 cos 2 α using the Pythagorean theorem, and square the entire equation. Move all the terms together on one side of the equation and set X = cosα. You are now facing a polynomial of degree 2 which can easily be solved. Last step, take the inverse cosine. You could do the same thing with the cosα term. 6
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